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This study simulates the flow properties of a plane-layered jet in free and impinging jets on a horizontal surface using Flow-3D and validates them with previous research and experimental data. The flow characteristics, such as velocity and shear stress distribution, are compared with theoretical relationships. The simulations vary the outlet velocities for the free jet and the surface types and slip conditions for the impinging jet. The results show that the free jet flow follows the self-similar theory, except for a faster decay of numerical velocities at the end of the jet's path. The results also reveal a virtual origin (λ) before the nozzle outlet, ranging from 7.6 to 8.4 mm. The impinging jet results match the experimental wall shear stress distribution diagram, with the peak at y/H = 0.14. The transverse velocity profiles and the wall shear stress distribution of the impinging jet are influenced by the slip condition and the surface type, but the difference between smooth and granular surfaces is less than 3%. This study offers valuable insights into the behaviour of free and impinging jets on a horizontal surface and shows the effectiveness of the Flow-3D numerical model. [ABSTRACT FROM AUTHOR]

In this article, a mathematical model is developed to study the effect of Non-Newtonian behavior of blood through stenosed artery considering Herschel-Bulkely fluid model. The constitutive equations of the model are solved analytically with the help of given boundary conditions to get different expression for flow rate. flow resistance and wall shear stress. It ix observed that the flow rate decreases with stenosis size. It has been shown that the resistance to flow and wall shear stress increases with the size of stenosis, but these increases is comparatively small due to Non-Newtonian type of blood and also comparison of these flow paraneters has been done for linear and quadratic variation of viscosity. [ABSTRACT FROM AUTHOR]

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier's slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries. [ABSTRACT FROM AUTHOR]

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier’s slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.

A comparative investigation is carried to examine the combined peristalsis and electroosmosis driven flow of silver-water nanofluid and silicon dioxide–water nanofluid through a porous medium. The fluid flow is taken through a symmetric flow channel. The flow problem is formulated mathematically under the influence mixed convection and heat source. No-slip conditions are employed across channel walls. Electroosmotic phenomenon is modeled through Poisson equation and Nernst –Planck equation. Debye-Hückel approximation is considered to obtain Boltzmann distribution of electric potential across electric double layer (EDL). Mathematical model is linearized subject to long wavelength and low Reynolds number assumption. Obtained system of equations are executed for exact solution. Impact of various involved parameters on flow properties is illustrated through graphical results.It is found that SiO2-water nanofluid moves faster than Ag-water nanofluid. Also temperature profile is lower for Ag-water nanofluid than that of SiO2-water nanofluid. Trapping phenomenon is thoroughly examined subject to electroosmosis. Helmholtz—Smoluchowski velocity parameter raises the fluid velocity for its negative values and velocity decays for its positive values. Reduction in thickness of EDL tends to increase the fluid velocity and decrease the pressure gradient. Fluid bolus disappears for thinner EDL.

A comparative investigation is carried to examine the combined peristalsis and electroosmosis driven flow of silver-water nanofluid and silicon dioxide–water nanofluid through a porous medium. The fluid flow is taken through a symmetric flow channel. The flow problem is formulated mathematically under the influence mixed convection and heat source. No-slip conditions are employed across channel walls. Electroosmotic phenomenon is modeled through Poisson equation and Nernst –Planck equation. Debye-Hückel approximation is considered to obtain Boltzmann distribution of electric potential across electric double layer (EDL). Mathematical model is linearized subject to long wavelength and low Reynolds number assumption. Obtained system of equations are executed for exact solution. Impact of various involved parameters on flow properties is illustrated through graphical results.It is found that SiO 2 -water nanofluid moves faster than Ag-water nanofluid. Also temperature profile is lower for Ag-water nanofluid than that of SiO 2 -water nanofluid. Trapping phenomenon is thoroughly examined subject to electroosmosis. Helmholtz—Smoluchowski velocity parameter raises the fluid velocity for its negative values and velocity decays for its positive values. Reduction in thickness of EDL tends to increase the fluid velocity and decrease the pressure gradient. Fluid bolus disappears for thinner EDL. [ABSTRACT FROM AUTHOR]

• An analytical solution is obtained for draining compressible fluid from a fracture. • The drainage rate is slip-like. • The drainage rate is proportional to the fluid's kinematic viscosity. Symmetric drainage flow of a compressible fluid from a thin fracture modeled as a long narrow 2D channel is studied on the basis of linearized compressible Navier-Stokes equations with the no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion; whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that, at large times, this no-slip flow exhibits a time-dependent slip-like mass flow rate linearly proportional to the channel gap instead of the cubic power of the gap for the Poiseuille-type of flow. The drainage rate is also proportional to the kinematic viscosity, opposite to Poiseuille-type of flow, which produces a drainage rate proportional to the inverse of the kinematic viscosity. The same drainage rate formula also applies to drainage flow from a semi-sealed thin fracture. [ABSTRACT FROM AUTHOR]

The main objective of this work is to predict the mixing of two different miscible oils in a very long channel. The background to this problem relates to the mixing of heavy and light oil in a pipeline. As a first step, a 2D channel with an aspect ratio of 250 is considered. The batch-mixing of two miscible crude oils with different viscosities and densities is modeled using an unsteady laminar model and unsteady RANS model available in the commercial CFD solver ANSYS-Fluent. For a comparison, a LES model was used for a 3D version of the 2D channel. The distinguishing feature of this work is the Lagrangian coordinate system utilized to set no-slip wall boundary conditions. The global CFD model has been validated against classical analytical solutions. Excellent agreement has been achieved. Simulations were carried out for a Reynolds number of 6300 (calculated using light oil properties) and a Schmidt number of 104. The results show that, in contrast to the unsteady RANS model, the LES and unsteady laminar models produce comparable mixing dynamics for two oils in the channel. Analysis of simulations also shows that, for a channel length of 100 m and a height of 0.4 m, the complete mixing of two oils across the channel has not been achieved. We showed that the mixing zone consists of the three different mixing sub-zones, which have been identified using the averaged mass fraction of the heavy oil along the flow direction. The first sub-zone corresponds to the main front propagation area with a length of several heights of the channel. The second and third sub-zones are characterized by so-called shear-flow-driven mixing due to the Kelvin-Helmholtz vortices occurring between oils in the axial direction. It was observed that the third sub-zone has a steeper mass fraction gradient of the heavy oil in the axial direction in comparison with the second sub-zone, which corresponds to the flow-averaged mass fraction of 0.5 for the heavy oil. [ABSTRACT FROM AUTHOR]

Abstract: An indirect boundary element method is proposed for the numerical solution of the Stokes equations in the axisymmetric case with Dirichlet and Neumann boundary conditions, which correspond to the velocity given on a part of the boundary and to the traction given on the other part. The method is described as applied to quasi-steady viscous creeping flows under gravity in regions bounded by a free surface and solid walls. A viscous fluid drop spreading over a hydrophobic horizontal surface is considered as an example. It is shown that the use of no-slip conditions ensure that the results have approximation convergence and satisfy the mass and energy conservation laws. [ABSTRACT FROM AUTHOR]

A numerical scheme is developed to simulate a flow around airfoils by using vortex methods. For this scheme, a numerical algorithm is constructed and exact analytical expressions are obtained for the coefficients of a system of linear algebraic equations. For some test problems, it is shown that the developed scheme allows us to solve a wider class of problems and provides much more accurate results in comparison with the known approaches. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model has been developed to analyze the fluid flow and heat transfer effect in a hydrophobic microchannel filled with a power law fluid. The effects of Joule heating, thermal radiation and velocity slip boundary conditions are analyzed by considering different slip parameters, EDL thickness, pressure gradient and flow behavior indices. The analytical expression for fluid flow and heat transfer have been derived in terms of the flow governing parameters based on the Debye-Huckel linearizing principle. Depending on the experimental existing flow behavior index, the analytical solutions are obtained in closed form where as numerical results are presented for general parametric values. The impact of slip velocity parameters in terms of a flow enhancement factor ( E fb ) , is studied to obtain the average flow velocity variation in a hydrophobic microchannel compared to a plane microchannel. The pressure assisted flow for pseudo-plastic (shear thinning) fluids achieve maximum velocity as compared to dilatant (shear thickening) fluids. The study finds that increase in thermal radiation minimizes heat transfer rate close to the hydrophobic wall, plays a vital role for the therapeutic treatment of hyperthermia (to understand the effect of heat transfer due to electric potential). It is also observed that Joule heating parameters enhance the heat transfer rate for classical Newtonian/non-Newtonian fluids for decrease in power indices and pressure gradient. [ABSTRACT FROM AUTHOR]

Recently, as the structural design has shifted to the performance design, seismic design of tunnel structures considering soil-structure interaction becomes more important. The effects of soil-structure interaction should not be overlooked for the reason that the interaction effects between a structure and surrounding ground may cause larger external forces to the structure. It has been highlighted that the relative rigidity between the soil and the structure is the predominant factor influencing the soil-structure interaction effects. With an aim to study the effects of tunnel-ground interaction, a number of analyses were carried out in this work, based on the most frequently used analytical expressions for evaluation of seismically induced stress increment in a tunnel lining accounting for the soil-structure interaction effects. These solutions are functions of the shear strain field which is the cause of the ovaling of the circular tunnel cross-section. A value of the average soil shear strain in the range of depths corresponding to the tunnel section, between the tunnel crown and the invert, has been computed through a free-field one-dimensional seismic site response analysis preformed by the code EERA. Various levels of analysis have been undertaken on different soil conditions, considering representative of two main soil classes - stiff soil of good conditions and soft saturated soil of poor conditions, as well as, two extreme cases of tunnel-ground interface - the full-slip and the no-slip conditions. Finally, the results for all the considered cases have been evaluated and compared, and the significant mutual differences with regard to a tunnel-ground interaction have been underlined.

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions. [ABSTRACT FROM PUBLISHER]

This paper develops a water holdup calculation model based on flow characteristics for no-slip oil-water two-phase flow. The model is constructed in consideration of two flow patterns: the stratified flow (ST) and the stratified flow with some mixing at the interface (ST&MI). The predicted values obtained by the model are compared with the test data on white oil-water flow. The results show that the model can accurately predict the water holdup of no-slip oil-water two-phase flow, which is of great significance for the determination of the working parameters in oilfields. [ABSTRACT FROM AUTHOR]

High solid dispersions are soft materials made of colloidal or non-colloidal particles dispersed at high volume fractions in a liquid matrix. They include hard sphere glasses, colloidal pastes, concentrated emulsions, foams, and vesicles. These materials are prone to exhibit different kinds of flow heterogeneities: shear banding, wall slip, and fracture. While wall slip is often considered as a nuisance by experimentalists, it appears to be a fundamental component to the way that high solid dispersions respond to mechanical deformation. Moreover, the ability of soft materials to slip onto surfaces allows them to move readily and efficiently in many natural phenomena and industrial processes. This review surveys recent developments and current research in the field. Topics like wall slip detection and control, microscopic modeling for rigid and soft particles materials, and the relation between wall slip and other flow heterogeneities are discussed. We also identify important open issues for future research. [ABSTRACT FROM AUTHOR]

We present numerical investigations of solidification around a cooled circular cylinder in the presence of forced convection. The numerical method is based on the front-tracking/finite difference and interpolation techniques. The solidification interface is represented by connected elements that move on a fixed, rectangular grid. The no-slip and Dirichlet temperature boundary conditions are imposed by the linear interpolation. The interpolation method was first validated through comparisons of the present results with some other numerical results for flow in an annulus, flow in an enclose with a conduction solid body and flow over a heated cylinder. We then used the method to investigate the solidification process around a cold cylinder by varying various parameters such as the Reynolds number Re, the Prandtl number Pr, the Stefan number, the thermal conductivity ratio k , the non-dimensional temperature of the introduced liquid θ , and the solid-to-liquid density ratio ρ . Numerical results indicate that an increase in any of Re, Pr and θ results in a decrease in the area of the solidification region around the cylinder. In contrast, increasing k increases the region of the solid phase. Investigation on St and ρ reveals that the solidification rate increases with an increase in St or a decrease in ρ . However, St and ρ have a minor effect on the final product of the solidification process. [ABSTRACT FROM AUTHOR]

A computational technique for applying wall boundary condition in dissipative particle dynamics simulation is presented. Based on the method first suggested by Willemsen et al. [14], the technique uses mirror image particles to naturally and effectively enforce the no-slip and no-penetration conditions. The technique is applied to the internal flows of various cross sectional shapes. The most important factor that ensures accurate application of the boundary conditions turns out to be the ratio of the narrowest gap between the facing walls to the particle diameter. When the ratio is sufficiently large, geometric features such as curvature, variation of curvature, and sharp corners can be well represented by the technique using mirror image particle. Also, by calibrating the size and direction of the shift in positions of image particle, spurious density oscillation near the boundary can be reduced while the velocity boundary conditions are sufficiently satisfied. [ABSTRACT FROM AUTHOR]

A systematic study is presented for the boundary layer Cattaneo–Christov double-diffusion model of heat and mass transfer in an upper-convected Maxwell nanofluid over a stretching sheet. The innovative constitutive model, namely Cattaneo–Christov upper-convected material derivative, is first introduced in characterizing the boundary layer slip shear flow, thermal diffusion and nanoparticles concentration diffusion. Viscoelastic relaxation framework system of upper-convected Maxwell nanofluid is constructed uniquely in which heat and mass transfer are both determined by Cattaneo–Christov model uniformly. The effects of Brownian motion & thermophoresis and the dynamic viscosity assumed as the linear function of temperature are taken into account. The highly coupled boundary layer governing equations including momentum, energy & mass conservation equations are transformed to similarity equations via appropriate dimensionless variables. The velocity, temperature & concentration distributions affected by respective relaxation parameters are obtained by homotopy analysis method (HAM) and analyzed thoroughly. Results indicated that this viscoelastic relaxation framework system makes us possible to predict the relaxation times transport characteristics. The internal elastic stress aggregates initially (with big skin friction) and then release (small stress) along with the development of the boundary layer, which is the main reason to generate macroscopic relaxation phenomena. Moreover, the effects of velocity slip on boundary layer transport are also discussed. [ABSTRACT FROM AUTHOR]

In this work, we use the homogenization theory to investigate the capability of wavy riblet patterns to influence the behaviour of a viscous flow near a ribbed boundary. Starting from perfect slip conditions on the wall, we show that periodic oscillations of wavy riblets in the lateral direction may induce a friction effect in the direction of the flow, contrary to what happens with straight riblets. Finally, we illustrate this effect numerically by simulating riblet profiles that are widely used in experimental studies: the V-shape, U-shape, and blade riblets. [ABSTRACT FROM AUTHOR]

In the present study, molecular dynamics (MD) simulation was used to investigate the relationship between wetting behaviour and slip length on patterned substrates. We adopted two solid surfaces of Si(100) and graphite due to similarities in their intrinsic contact angle. Contact angle and apparent slip length were obtained using discrete simulations with the same thermodynamic states. In the present study, a number of questions regarding surface roughness and the problem of contact angle (θ) and slip length (Ls) are discussed. These questions include the relationship between θ and surface roughness, the characteristics used to describe the difference between static and dynamic fluid fields and the reason for a lack of multilayer sticking observed in the current cases. Our results indicate that the quasi-universal θ −Lsequation proposed by Hunget al. (2008) is applicable to cases involving a Cassie-like nanoscale roughened surface. In contrast, in cases with a Wenzel-like nanostructure, the no-slip boundary conditions are independent of variations in the contact angle. The adoption of a Wenzel–Cassie hybrid model helped to verify that the fluid density inside the cavity is a critical indicator of wettability of the wall–fluid interface. Our results also demonstrate that ρf, cavis a critical property in the measurement of hydrodynamic effects and thus its importance as an indicator of the validity of the equation θ −Ls. The average time that water molecules are trapped and the number of averaged hydrogen bonds within cavities in a dynamic fluid field were also investigated.   [ABSTRACT FROM AUTHOR]

The trajectory of a spherical magnet that rolls without slipping on a conductive plate is modeled. A time-stepping \vec T-\Omega method is used to find the electromagnetic force and the torque on the magnet. Since the degrees of freedom involve both the position and the direction of magnetization of the spherical magnet, the motion here cannot be reduced to the calculation of a single friction force coefficient. The trajectory of the spherical magnet is computed and compared with our experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a method that combines the characteristic-based split finite element method (CBS-FEM) and the direct forcing immersed boundary (IB) method is proposed for the simulation of incompressible viscous flows. The structured triangular meshes without regarding the location of the physical boundary of the body is adopted to solve the flow, and the no-slip boundary condition is imposed on the interface. In order to improve the computational efficiency, a grid stretching strategy for the background structured triangular meshes is adopted. The obtained results agree very well with the previous numerical and experimental data. The order of the numerical accuracy is shown to be between 1 and 2. Moreover, the accuracy control by adjusting the number density of the mark points purely at certain stages is explored, and a second power law is obtained. The numerical experiments for the flow around a cylinder behind a backward-facing step show that the location of the cylinder can affect the sizes and the shapes of the corner eddy and the main recirculation region. The proposed method can be applied further to the fluid dynamics with complex geometries, moving boundaries, fluid-structure interactions, etc.. [ABSTRACT FROM AUTHOR]

Oneof the central dogmas of fluid physics is the no-slip boundarycondition, whose validity has come under scrutiny, especially in thefields of micro and nanofluidics. Although various studies show theviolation of the no-slip condition its effect on flow of colloidalparticles in viscous media has been rarely explored. Here we reportunusually large reduction of effective viscosity experienced by polymericnano colloids moving through a highly viscous and confined polymer,well above its glass transition temperature. The extent of reductionin effective interface viscosity increases with decreasing temperatureand polymer film thickness. Concomitant with the reduction in effectiveviscosity we also observe apparent divergence of the wave vector dependenthydrodynamic interaction function of these colloids with an anomalouspower law exponent of ∼2 at the lowest temperatures and filmthickness studied. Such strong hydrodynamic interactions are not expectedfor polymeric colloidal motion in polymer melts. We suggest hydrodynamics,especially slip present at the colloid–polymer interface whichdetermines the observed reduction in interface viscosity and presenceof strong hydrodynamic interactions. [ABSTRACT FROM AUTHOR]

In the axisymmetric approximation the problem of spreading lava as an incompressible constant-viscosity liquid over a flat horizontal surface is solved. Instead of the classical no-slip condition, a condition of partial lava slip along the underlying surface is used: at the surface the velocity is assumed to be a power function of friction. In the thin-layer approximation, for the problem of slow liquid spreading an asymptotic self-similar solution is constructed on the assumptions of partial slip along the underlying surface and a power time dependence of the flow rate. The same problem is solved in the complete formulation numerically. It is shown that the numerical and asymptotic solutions are in good agreement. It is established that with account for the slip effect the lava propagation velocity may be substantially higher than for the no-slip condition. [ABSTRACT FROM AUTHOR]

In the present paper the results of numerical modeling of peristaltic flow of a Carreau fluid in a vertical asymmetric channel are presented. The effects of slip and heat transfer have been analyzed. Using the approximation of long wavelength, low Reynolds number and with the suitable dimensionless variables, the reduced equations have been solved analytically by regular perturbation method. The expressions for velocity, stream function, temperature, pressure gradient and pressure rise have been computed which strongly depend on the physical parameters of the Carreau fluid. With the help of analytical results the expression for pressure rise has been computed using numerical integration scheme. To reveal the tendency of the solutions, typical results for velocity, temperature, stream function, pressure gradient and pressure rise are presented for different values of controlling parameters. [ABSTRACT FROM AUTHOR]

For the transition from slip- to no-slip fluid flow, we establish lower and upper bounds to the resulting change of the L²-norm of the vorticity. Moreover we present a transport-diffusion splitting scheme, built up solely by a transport step and subsequent diffusion step (without any additional vorticity creation operator as introduced in former studies by Lighthill, Marsden, and Chorin), the splitting scheme being consistent with the Navier-Stokes equations with no-slip condition. [ABSTRACT FROM AUTHOR]

A plane steady problem of a point vortex in a domain filled by a viscous incompressible fluid and bounded by a solid wall is considered. The existence of the solution of Navier-Stokes equations, which describe such a flow, is proved in the case where the vortex circulation Θ and viscosity ν satisfy the condition |Θ| < 2 πν. The velocity field of the resultant solution has an infinite Dirichlet integral. It is shown that this solution can be approximated by the solution of the problem of rotation of a disk of radius Γ with an angular velocity ω under the condition 2 πγ ω → Γ as γ → 0 and ω→∞. [ABSTRACT FROM AUTHOR]

Exact analytical solutions of the problem of flow past a sphere and a cylinder in a porous medium are derived within the framework of the Brinkman equationwith the Navier boundary condition. Attention is drawn to the fact that the no-slip condition imposed on the interface between the porous medium and a solid, used, in particular, in the case of the Brinkman equation, must be in the general case replaced by a condition that admits nonzero flow velocity at the boundary. [ABSTRACT FROM AUTHOR]

Abstract: The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter. [Copyright &y& Elsevier]